Efficiency evaluation for the nested cube response surface design

Abstract

The nested cube response surface design is defined and its attributes described.Variance, bias and potential estimators are evaluated for the nested cube design.The standard least-squares estimator is examined for the quadratic and cubic models.Estimable parameters in the cubic model are derived for the nested cube design as well as a set of select designs.A minimum bias estimator is examined where the true model is cubic and the fitted model is quadratic.The nested cube design was the only design of the set examined for which the estimator existed.Two measures of bias efficiency are introduced and used to compare the nested cube design to a set of selected designs.Variance efficiency is evaluated in terms of A-, V-, and D-efficiencies.A calculation formula for the determinant of the sum of squares matrix is derived for symetric designs with zero odd moments.Profiles of the variance are shown on selected vectors in the region of interest........

Cite this paper

@phdthesis{linnell2015efficiency,
  title = {{Efficiency evaluation for the nested cube response surface design}},
  author = {Linnell, Melvin Gail},
  school = {Montana State University ScholarWorks (Montana State University)},
  year = {2015}
}

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